Find the Taylor Series at X = 0 of the Function

question 4

Multiple Choice

Find the Taylor series at x = 0 of the function f(x) = $\frac { 1 } { 1 - 3 x }$ by computing three or four derivatives and using the definition of the Taylor series.

• A) 1 - 3x + 9 \(x ^ { 2 }\) - 27 \(x ^ { 3 }\) + ...
• B) 1 + 3x + 9 \(x ^ { 2 }\) + 27 \(x ^ { 3 }\) + ...
• C) 1 + \(\frac { 3 x } { 1 }\) x + \(\frac { 9 x } { 2 }\) \(x ^ { 2 }\) + ...
• D) 1 + \(( 3 x ) ^ { 2 }\) + \(( 3 x ) ^ { 4 }\) + \(( 3 x ) ^ { 6 }\) + ...
• E) none of these

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